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arXiv · 1603.01693

Dessins on Modular Curves

Khashayar Filom·Ali Kamalinejad
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Abstract

Given a finite index subgroup $\Gamma$ of ${\rm{PSL}}_2(\Bbb{Z})$, we investigate Belyi functions on the corresponding modular curve $X(\Gamma)$ by introducing two methods for constructing such functions. Numerous examples have been worked out completely and as an application, we have derived modular equations for $\Gamma_0(2),\Gamma_0(3)$ and several special values of the $j$-function by a new method based on the theory of Belyi functions and dessin d'enfants.

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Khashayar Filom, Ali Kamalinejad. 2016-03-05. Dessins on Modular Curves. https://arxiv.org/abs/1603.01693

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